Confusion about properties of linear transformation.I learned from 3Blue1Brown's Linear Algebra videos that one of the rules for a transformation to be linear is that the origin remains fixed in place after transformation. So if T(x)=x+a is a given transformation, I know that by inserting x=0, it is not a linear transformation. I am not able to understand what is non-linear about it.

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Confusion about properties of linear transformation.I learned from 3Blue1Brown&#039;s Linear Algebra videos that one of the rules for a transformation to be linear is that the origin remains fixed in place after transformation. So if T(x)=x+a is a given transformation, I know that by inserting x=0, it is not a linear transformation. I am not able to understand what is non-linear about it.

Layla Humphrey · Accepted Answer

Because T(0+0)=a, whereas T(0)+T(0)=2a, which is different from a (unless a=0, of course). But one should have T(0+0)=T(0)+T(0) if T was linear.

monogamab0f · Accepted Answer

If a≠0,then T(0)≠0. The transformation is what we call affine, but not strictly linear.

Confusion about properties of linear transformation.I learned from 3Blue1Brown's Linear Algebra videos that one of...

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